Control of dynamic sp3-C stereochemistry

Stereogenic sp3-hybridized carbon centres are fundamental building blocks of chiral molecules. Unlike dynamic stereogenic motifs, such as sp3-nitrogen centres or atropisomeric biaryls, sp3-carbon centres are usually fixed, requiring intermolecular reactions to undergo configurational changes. Here we report the internal enantiomerization of fluxional carbon cages and the consequences of their adaptive configurations for the transmission of stereochemical information. The sp3-carbon stereochemistry of the rigid tricyclic cages is inverted through strain-assisted Cope rearrangements, emulating the low-barrier configurational dynamics typical for sp3-nitrogen inversion or conformational isomerism. This dynamic enantiomerization can be stopped, restarted or slowed by external reagents, while the configuration of the cage is controlled by neighbouring, fixed stereogenic centres. As part of a phosphoramidite–olefin ligand, the fluxional cage acts as a conduit to transmit stereochemical information from the ligand while also transferring its dynamic properties to chiral-at-metal coordination environments, influencing catalysis, ion pairing and ligand exchange energetics.

Stereogenic sp 3 -hybridized carbon centres are fundamental building blocks of chiral molecules. Unlike dynamic stereogenic motifs, such as sp 3 -nitrogen centres or atropisomeric biaryls, sp 3 -carbon centres are usually fixed, requiring intermolecular reactions to undergo configurational changes.
Here we report the internal enantiomerization of fluxional carbon cages and the consequences of their adaptive configurations for the transmission of stereochemical information. The sp 3 -carbon stereochemistry of the rigid tricyclic cages is inverted through strain-assisted Cope rearrangements, emulating the low-barrier configurational dynamics typical for sp 3 -nitrogen inversion or conformational isomerism. This dynamic enantiomerization can be stopped, restarted or slowed by external reagents, while the configuration of the cage is controlled by neighbouring, fixed stereogenic centres. As part of a phosphoramidite-olefin ligand, the fluxional cage acts as a conduit to transmit stereochemical information from the ligand while also transferring its dynamic properties to chiral-at-metal coordination environments, influencing catalysis, ion pairing and ligand exchange energetics.
The hugely varied three-dimensional (3D) structures-and therefore the hugely varied properties-of many organic molecules emerge from combining just a few types of atomic building blocks. For example, 19 of the 22 proteinogenic amino acids are formed solely from sp 2 -or sp 3 -hybridized carbon, nitrogen and oxygen atoms, capped by hydrogen substituents. Of this small array of elemental building blocks, it is tetrahedral sp 3 -carbon [1][2][3][4] and sp 3 -nitrogen [5][6][7][8][9][10] atoms that have the potential to form stereogenic centres, creating chiral structures.
Instead, intermolecular reactions are usually necessary 20,21 to invert individual stereogenic carbon centres, proceeding through mechanisms involving high-energy bond-breaking and bond-making steps 22 with pentavalent transition states 20 (for example, S N 2 reactions) or trigonal intermediates 21 , such as carbocations, carbanions or radicals. Of course, it is this stability of sp 3 -carbon's tetrahedral geometry that makes it essential to the chiral skeletal diversity of organic compounds. It allows for predictable synthesis of configurationally stable molecules. Yet, the stability also limits the extent to which the complex 3D connectivity of aliphatic structures can exhibit dynamic, adaptive stereochemistry 23 .
There have been impressive, but rare, examples of small covalent systems 24-28 capable of sp 3 -carbon enantiomerization by low-barrier intramolecular processes. However, they do so without external control of their rate or direction to a single stereoisomer. Only multicomponent interlocked molecules, in which a ring shuttles along a prochiral axle 29,30 , have been amenable to external control. There have been no compact and controllable dynamic sp 3 -carbon building blocks. Therefore, it has not been possible to investigate the transmission of stereochemical information through such systems 7,9,10 .
In this Article we report a series of chiral fluxional carbon cages 26-29 that exhibit responsive sp 3 -carbon-centred stereochemistry, adapting to and transmitting surrounding stereochemical information.

Diastereomeric adaptation
We targeted 9-BB 1 (Fig. 2) as a convenient example of the 9-BB substitution pattern that bears a hydroxyl group for synthetic elaboration. The Cope rearrangement involving positions 2-8 of 1 (Fig. 2a) causes enantiomerization of the whole cage and formally inverts the stereochemistry of position 9 by effectively 'swapping' the cyclopropyl and alkene substituents connected to the stereocentre. Compound 1 was synthesized (Supplementary Scheme 1) by a three-step route from ethynyl magnesium bromide and tropylium tetrafluoroborate, using a gold-catalysed enyne cycloisomerization 39,40 to form the BB backbone. When labelling 1 and subsequent compounds, a single stereochemical descriptor is included to indicate the configuration at position 9 of the BB (Fig. 2a), for example, (R)-1 and (S)-1, omitting the additional stereochemical labels of positions 1, 2, 5 and 8 for simplicity (Fig. 1). Treatment of 1 with Mosher's acid chloride (Fig. 2a) produces a set of Mosher's esters 2 in which the configurationally fixed stereocentre is introduced at a distance of three covalent bonds from the dynamic BB unit. An additional descriptor for the configuration of the Mosher's ester group is included in the labels for 2. Derivatization with (S)-Mosher's acid gives a dynamic mixture of two diastereomers, (R,S)-2 and (S,S)-2, whereas (R)-Mosher's acid gives (Fig. 2a) the antipodal mixture, (S,R)-2 and (R,R)-2. Solutions of the two antipodal dynamic mixtures give opposite circular dichroism spectra (Fig. 3a), as would be expected.
DFT modelling using the ωB97X-D functional 41 , 6-311++G(d,p) basis set 42,43 and a CS 2 polarizable continuum solvent model using the integral equation formalism variant 44 was employed to compare (Supplementary Table 7) the stereoisomerization energetics of BB, 1 and 2. Using these parameters, the automerization of BB is predicted to proceed with a calculated activation free energy, ΔG ‡ calc , of 38.5 kJ mol −1 , which is ~6 kJ mol −1 higher than the experimentally measured 35 activation free energy, ΔG ‡ exp , of 32.3 kJ mol −1 , in keeping with previous DFT investigations 36,37 . DFT methods systematically overestimate the energy barrier to Cope rearrangement of BBs, but nevertheless allow useful comparisons of trends in activation energies and are known to predict accurately the relative energy minima of isomers 36,37 . The computationally predicted ΔG ‡ calc values for 1 (38.0 kJ mol −1 ) and 2 (35.5 kJ mol −1 ) are very similar to BB, indicating that the hydroxyl or ester group substitutions at position 9 do not appreciably change the rapid kinetics.
The absence of the ′′ v mirror plane in 1 is evident (Fig. 3b) in its solution-state 1 H NMR spectrum-H3 and H7 are magnetically inequivalent, for example. However, the rapid enantiomerization induces a ′ v mirror plane to the time-averaged structure of 1, so only six distinct methine resonances are observed overall. The additional, fixed stereocentre of 2 breaks this ′ v symmetry. Consequently, nine distinct signals corresponding to the BB methine groups are observed (Fig. 3b).
An energy difference, ΔG calc , of 4.5 kJ mol −1 is computed (Supplementary Table 7) for the rearrangement of 2. The influence of the (S)-Mosher's ester group moulds the configuration of the cage unit, which preferentially adopts its S form, biasing the equilibrium towards (S,S)-2. Consistent with this prediction, a single crystal (Fig. 2a) obtained from the dynamic (S)-Mosher's ester mixture was found to contain (S,S)-2 as a frozen 34 , single stereoisomer. An equal and opposite outcome is observed from the (R)-Mosher's ester mixture, giving the enantiomeric (R,R)-2 solid-state structure.
To establish the nature of the dynamic solution-state mixtures, we compared (Fig. 3c) the solid-state 13 C{ 1 H} NMR spectrum of enantiopure (R,R)-2 crystals to a spectrum obtained using a sample of the (S,S)-2 crystals dissolved in 5:1 CS 2 -CD 2 Cl 2 , generating a dynamic mixture of (R,S)-2 and (S,S)-2. Cooling the solution to 159 K causes the BB 13 C{ 1 H} NMR resonances to enter the slow exchange regime.
By applying density functional theory (DFT) calculations and solutionand solid-state NMR spectroscopy, in combination with X-ray crystallography, we establish the extent to which their dynamic Cope rearrangements 31,32 are controlled by neighbouring, fixed stereogenic centres. We have found that a substantial energetic bias of more than 10 kJ mol −1 can be exercised over the stereochemical equilibria by a single fixed stereocentre. The rearrangements proceed rapidly at rates more commonly associated with low-barrier conformational changes of aliphatic systems (for example, a cyclohexane ring-flip energy barrier of ~43 kJ mol −1 ) rather than a configurational change. We show that these rapid constitutional dynamics can be halted by covalent modification of the cage through a [2 + 2 + 2] cycloaddition reaction, then subsequently restarted after a cycloreversion. The rearrangement rate is also attenuated upon coordination of the fluxional cage to Pd(II) or Ru(II) as part of a phosphoramidite-olefin ligand. By its inclusion in the simple ligand design, the fluxional cage transmits stereochemical information to the metal ion-either through the covalent ligand backbone or by ion pairing with a chiral counterion. This property is exploited in enantioselective catalysis of an allylic substitution reaction, as well as in creating chiral-at-metal stereogenic centres that adopt the configurational dynamics of the cage.

Results
The Cope rearrangement of barbaralane (BB) is an example (Fig. 1a) of a narcissistic 25,33 automerization-it gives rise to a degenerate structure through a transition state (TS-BB) bearing an internal mirror plane ( ′ v ) that is not present in the minimum energy structure. We noted that by desymmetrizing BB (Fig. 1b) using either a 9-BB, 3-BB or 2,4-BB substitution pattern, the mirror plane present at the energy minimum ( ′′ v ) is lost, while the mirror plane formed in the transition state ( ′ v ) is retained. As a result, the Cope rearrangement inverts simultaneously some, or all, of the four or five stereogenic centres present in the structure. Given that the rearrangement of BB is known to proceed with a Cahn-Ingold-Prelog priorities are chosen to be R 1 > C > R 2 for the assignment of absolute configuration. When assigning a descriptor to position 9 of 9-BB, the cyclopropyl bridgehead C1 has precedence over the divinyl bridgehead C5 (Supplementary Fig. 1). 3-BB and 2,4-BB each have four chirotopic (R/S) centres, whereas the 9-BB pattern gives rise to five stereogenic centres, of which three are chirotopic and two are achirotopic (r/s).
Article https://doi.org/10.1038/s41557-023-01156-7 As 159 K is only ~20 K below the observed coalescence temperature ( Supplementary Fig. 66) for this low-barrier process, some resonances exhibit exchange broadening. At this low temperature, the decrease of available thermal energy causes the Boltzmann distribution to shift (Fig. 3d) further towards the lowest-energy isomer 34 . The solid-state chemical shifts of the BB sp 3 -carbons 1, 2, 5, 8 and 9 are assigned ( Fig. 3b) by comparison to the calculated chemical shifts of (R,R)-2. The resonances of the solution sample match up well with those of (R,R)-2 in the solid state, allowing us to assign the resolved solution-state diastereomer as (S,S)-2. The solution-state analysis is thus consistent with the diastereomeric preference predicted by DFT and observed in the solid state. The 9-BB cage undergoes dynamic diastereomeric adaptation under the influence of the configurationally fixed Mosher's ester group.
The dynamic stereochemical equilibrium can also be biased in the absence of a fixed stereogenic element. Dimerization of two 9-BB-type cages through a spirocylic linkage breaks the degeneracy of the equilibrium. By treating (Fig. 2b) barbaralone 3 with Lawesson's reagent, we isolated trithiolane 4, which undergoes dynamic rearrangements between an achiral isomer, meso-4, and a pair of enantiomers, (S,S)-4 and (R,R)-4. A small ΔG calc of 0.7 kJ mol −1 is predicted (Supplementary Table 7) to favour the pair of enantiomers over the meso form in the solution state. Single crystals grown from a solution of 4 contain a racemic mixture of the two chiral stereoisomers. S R Further chemical modification to the substituent at position 9 can substantially influence, and even invert, the cage's equilibrium distribution. The chiral phosphoramidite-olefin [45][46][47] ligand L BB1 was synthesized (Fig. 2c) by first subjecting 3 to reductive amination with (S)-1-phenylethylamine to afford a mixture of (S,S)-5 and (R,S)-5. Sequential treatment of the amine with PCl 3 then 2,2′-methylenediphenol affords L BB1 . The 2,2′-methylenediphenol functionality was selected as it lacks fixed stereochemistry but has been shown to adopt dynamically chiral conformations as part of phosphoramidite ligands 45 . Comparing L BB1 to 5 reveals that the differing size and shape of the substituent at position 9 drives the dynamic stereochemical equilibria of the fluxional cage towards opposite configurations. The solution-phase equilibrium of the secondary amine is weighted (Supplementary Table 7) towards the (R,S)-5 diastereomer by a ΔG calc of 3.8 kJ mol −1 , matching the structure observed by X-ray analysis (Fig. 2c) of a single crystal. By contrast, the (S,S)-L BB1 diastereomer of the phosphoramidite is favoured with a ΔG calc of 20.2 kJ mol −1 . The large magnitude of ΔG calc for L BB1 highlights that the configurational dynamics of the 9-BB motif ( Fig. 1) correlate with notable changes in its 3D shape 34 and, therefore, its energy. At the same time, the opposing stereochemistry of cages 5 and L BB1 demonstrates that the malleable sp 3 -carbon configuration adapts to changes in the nearby steric environment.

Manipulating rates and transfer of stereochemistry
To exert further control over the fluxional enantiomerization, we sought to exploit the reactivity of the BBs' skipped diene units. The fluxional rearrangements can be stopped entirely by engaging the alkene units in covalent bonding, whereas coordination of the π electrons to a transition-metal ion 38 modulates the rearrangement rate instead.
An enantiomerizing mixture of 9-(p-tolyl)barbaralol 6 engages (Fig. 2d) in a [2 + 2 + 2] cycloaddition reaction with phenyl-1,2, 4-triazoline-3,5-dione 48 , giving rise to 7. This reaction halts the rearrangement while also symmetrizing the structure by forming a second cyclopropyl group. Subsequently, the fluxional cage can be regenerated (Fig. 2d) in a two-step transformation through diazinane 8 ( Supplementary Fig. 62), which undergoes cycloreversion with loss of N 2 upon oxidation with CuCl 2 . Alternatively, coordination of Pd(II) (Fig. 4) or Ru(II) (Fig. 5) to L BB1 causes a reduction in the rate of the Cope rearrangement, as discussed below. L BB1 and PdCl 2 form (Fig. 4a) a chiral-at-metal 49,50 complex, L BB1 PdCl 2 , linking the sp 3 -carbon configurational inversion to the A/C isomerism 51 of the distorted trigonal bipyramidal (TBPY-5-12) coordination environment (Supplementary Fig. 2). Both possible stereoisomers, arising from coordination of (S,S)-L BB1 or (R,S)-L BB1 through their phosphorus centre and an alkene, are observed (Fig. 4a) in the X-ray crystal structure of the L BB1 PdCl 2 complex. The alkene coordination is also evident (Fig. 4b) in the solution state by 1 H NMR spectroscopy. For comparison, a monodentate L BB1 AuCl complex (Fig. 4a) was prepared, which shows only small changes in the 1 H NMR chemical shifts of its alkene signals H3 and H7 relative to the free ligand (Fig. 4b). The room-temperature spectrum of L BB1 PdCl 2 , on the other hand, reveals a large change in the chemical shift of H7, consistent with coordination of Pd(II) to the alkene on the same face as the phosphoramidite group.
At 240 K, the 1 H NMR spectrum reveals (Fig. 4b) the two L BB1 PdCl 2 isomers in slow exchange. Two sets of signals are observed in a 3:4 ratio, corresponding to a small free energy difference, ΔG exp , of 0.5 kJ mol −1 between the two isomers. Consistent with this observation, DFT calculations predict (Supplementary Table 7) a small ΔG calc of 1.8 kJ mol −1 in favour of (C,R,S)-L BB1 PdCl 2 .
Further NMR and DFT analyses elucidate the mechanism by which the L BB1 PdCl 2 complex isomerizes. Depending on the placement and nature of substituents around the Cope substrate, metal coordination can either stabilize a charged, intermediate species as part of a stepwise associative rearrangement mechanism, or it can increase the rate of a concerted rearrangement pathway by stabilizing the transition state 52 . Consequently, Pd(II) salts and other cationic metal ions are known to accelerate Cope rearrangements 53,54 . Remarkably, coordination of the Pd(II) to one face of the fluxional cage in L BB1 PdCl 2 has the opposite effect, slowing down the Cope rearrangement. Unlike 2, for example, whose 1 H NMR resonances (499 MHz) enter the slow exchange regime below 160 K ( Supplementary Fig. 64), the slower rearrangement of L BB1 PdCl 2 is resolved by 1 H NMR spectroscopy at the higher temperature of 240 K. Using 2D 1 H-1 H exchange spectroscopy (EXSY) at 240 K (Fig. 4c), we measured a rate of exchange, k, of 6.48 s −1 , indicating a ΔG ‡ exp of 54.6 kJ mol −1 for L BB1 PdCl 2 (Fig. 4d). The DFT-calculated transition-state structure (Fig. 4e) shows pairs of equidistant C-C bonds, as would be expected for a coordination-coupled Cope (cc-Cope) rearrangement (Fig. 4a) in which the Pd(II) remains bound to the cage through a concerted rearrangement step. The DFT-predicted  Fig. 2. c, Comparison of partial 13 C{ 1 H} NMR spectra: top, solid-state chemical shifts calculated from the X-ray crystal structure of (R,R)-2 in CASTEP v17.2 65 using the Perdew-Burke-Ernzerhof functional 66 and on-the-fly generated pseudopotentials; middle, (R,R)-2 as a powder at ambient temperature (105 MHz); bottom, (S,S)-2 as a solution in 5:1 CS 2 -CD 2 Cl 2 at low temperature (125 MHz, 159 K). The asterisk indicates the resonance of residual acetone. d, The Boltzmann distribution of isomers shifts towards a single stereoisomer at low temperatures; for example, a free energy difference of ~5 kJ mol −1 would give an ~90:10 equilibrium mixture at room temperature, but >98:2 at 159 K, so NMR data would be expected to show a single, major species, as is apparent when comparing the three spectra in c.
Article https://doi.org/10.1038/s41557-023-01156-7 ΔG ‡ calc of 60.6 kJ mol −1 for this cc-Cope mechanism matches well with the ΔG ‡ exp of 54.6 kJ mol −1 . These data indicate that the metal ion 'walks' along one side of the BB cage as the Cope rearrangement proceeds, moving back and forth in sync with the pericyclic reaction 52 . Consequently, the BB not only transmits the stereochemical information from the fixed sp 3 -carbon stereocentre through its dynamic sp 3 -carbon framework, biasing the chiral-at-metal configuration, but it also imparts a novel mechanism of intramolecular configurational change at a pentavalent stereocentre, which differs from the established pseudorotation and turnstile mechanisms 55 .
Ru(II) coordination slows the Cope rearrangement sufficiently for a single stereoisomer to be resolved as a metastable species under ambient conditions (Fig. 5b). Upon dissolving single crystals of L BB1 RuCp(NCMe)·PF 6 , obtained by slow evaporation, the 1 H NMR spectrum shows the presence of a single complex (Fig. 5b) with resonances distinct from non-coordinated L BB1 . After allowing the sample to fully equilibrate at room temperature for four hours, a new set of peaks is observed (Fig. 5b) at a ratio of 4:1 in favour of the initially observed isomer, equivalent to a ΔG exp of 4.0 kJ mol −1 . X-ray analysis (Fig. 5c) of the crystalline sample reveals the identity of the energetically favoured isomer to be (C,R,S)-L BB1 RuCp(NCMe)·PF 6 .
We measured the isomerization rate of (C,R,S)-L BB1 RuCp(NCMe)·PF 6 by monitoring (Fig. 5d) the first-order growth in intensity of the resonance at 3.1 ppm corresponding to the H9′ signal of (A,S,S)-L BB1 RuCp (NCMe)·PF 6 -the isomer calculated (Fig. 5e) to be the next most stable stereoisomer. The k obs of 2.56 × 10 −3 s −1 at 298 K allows us to determine a ΔG ‡ exp of 87.8 kJ mol −1 . Comparison of this value to (1) maxima of the computed potential energy surface (Fig. 5e), (2) a CD 3 CN exchange experiment ( Supplementary Fig. 70) and (3) literature measurements of MeCN dissociation from Cp half-sandwich Ru(II) complexes 55 suggests that the cc-Cope and MeCN exchange processes occur at similar rates. To achieve the (C,R,S)-to-(A,S,S) isomerization observed by NMR, the complex must undergo both ligand exchange and cc-Cope steps (Fig. 5e). Overall, the energetic bias towards (C,R,S)-L BB1 RuCp(NCMe)·PF 6 and observation of its stepwise stereomutation to (A,S,S)-L BB1 RuCp (NCMe)·PF 6 illustrate that the fluxional sp 3 -carbon cage mediates the transfer of stereochemical information with high fidelity from the single, fixed benzylamino stereocentre through its rigid, tricyclic structure.

Dynamic stereocontrol by ion pairing
Having observed transmission of stereochemical information within the covalent frameworks of the L BB1 complexes, we investigated the influence of chiral counterions 57 on the degenerate enantiomerization (Fig. 6a) of the cationic L BB2 RuCp(NCMe) + complex, which lacks a fixed stereocentre in its ligand structure. The complex was synthesized (Supplementary Scheme 3) as its hexafluorophosphate salt, L BB2 RuCp(NCMe)·PF 6 , in a manner analogous to its permanently chiral homologue L BB1 RuCp(NCMe)·PF 6 (Fig. 5). X-ray analysis of single crystals confirmed (Supplementary Fig. 94) the expected structure of L BB2 RuCp(NCMe)·PF 6 and revealed the presence ( Supplementary  Fig. 95) of both the (C,R)-and (A,S)-isomers in the crystal unit cell.
In the absence of chiral anions, a single 1 H NMR signal is observed for the coordinated MeCN ligand of L BB2 RuCp(NCMe)·PF 6 in CDCl 3 solution (Fig. 6b). However, the addition of one molar equivalent of a chiral shift reagent, Bu 4 N·Δ-TRISPHAT 58 (Fig. 6b) or Na·(S)-BORBIN 59 ( Supplementary Fig. 71), splits the signal in two. Rapid and reversible counterion exchange in the presence of Bu 4 N·Δ-TRISPHAT establishes an equilibrium mixture that includes diastereomeric ion pairs, for example, (C,R)-L BB2 RuCp(NCMe)·Δ-TRISPHAT and (A,S)-L BB2 RuCp(NCMe)·Δ-TRISPHAT, which give distinct NMR resonances. Therefore, by tracking the relative intensities of these resonances over time ( Fig. 6b and Supplementary Fig. 72) we can monitor changes in sample composition as the chiral anion biases the L BB2 RuCp(NCMe) + complex towards one stereoisomer. Under these conditions, the Δ-TRISPHAT sample evolves from a 1:1 mixture of stereoisomers to a Article https://doi.org/10.1038/s41557-023-01156-7 1:0.81 mixture over several hours, corresponding to an equilibrium constant, K, of 1.2, and ΔG exp ≈ 0.5 kJ mol −1 . The timeframe of the sample's evolution is consistent with the slow kinetics of isomerization measured (Fig. 5) for L BB1 RuCp(NCMe)·PF 6 , suggesting that the stereomutation is again proceeding by cc-Cope and MeCN ligand exchange. The (S)-BORBIN sample reaches (Supplementary Fig. 72) a K of 1.3 over a similar time period. Overall, these experiments establish a means of noncovalent control of the BB stereochemistry. In principle, K could be further increased by removal or omission of any competing achiral anions (such as PF 6 − ) from the reaction mixture and optimization of solvent and concentration.
Based on these results, we hypothesized that this counteriondirected stereochemistry of cationic L BB2 complexes could be exploited in enantioselective ion-pair catalysis 60 . Unusually, the fixed stereochemistry of the chiral anion would be passed to the catalytically active, fluxional metal complex to transiently generate an enantioenriched ligand framework in situ. To probe this concept, we screened L BB2 and two control ligands (Fig. 6c) in the enantioselective synthesis of 9 (Fig. 6d) through iridium-catalysed allylic substitution of alcohol 10 by hydroxycoumarin 11 61 . We used chiral phosphoric acid (R)-BDHP, which we expected to protonate 10 and induce formation of the iridium-stabilized allylic cation intermediate while simultaneously generating an equivalent of a chiral phosphate anion. The optimized literature conditions 61 for this allylic substitution employ an achiral Lewis acid (Yb(OTf) 3 ) rather than a Brønsted acid to generate the allylic cation, in conjunction with enantiopure Carreira's 46 phosphoramiditeolefin ligand, CL, to impart enantioselectivity. Pleasingly, replacing these reagents with (R)-BDHP and racemic (±)-CL leads to the formation of 9, albeit in just 14% isolated yield. Importantly, however, there is essentially no enantioinduction under the influence of (±)-CL. The product is obtained with a negligible enantiomeric excess (e.e.) of just 2%. It appears that the chiral phosphoric acid alone does little to override the stereochemical preference (or overall lack of it) arising from the racemic ligand. Using achiral phosphoramidite-olefin ligand L CP leads to a similar outcome. L CP bears many of the same structural features of L BB2 , but with an achiral cyclopentene unit in place of the dynamically chiral 9-BB substructure. Compound 9 is produced in 49% yield and just 2% e.e. using L CP . Conversely, our fluxionally chiral ligand, L BB2 , delivers an improved e.e. Using L BB2 , we isolated 9 in 36% yield and 30% e.e. Contrasting this result with the outcome of the reactions using L CP and (±)-CL supports the idea that the chiral phosphate counterion biases the covalent L BB2 ligand stereochemistry of the cationic intermediate complex (Supplementary Scheme 5), which in turn improves the enantioinduction in the key bond-forming step. Although the resulting e.e. is moderate for this particular set of reaction conditions, it suggests that the use of fluxional sp 3 -carbon units may enhance the design of ligand frameworks for ion-pair catalysis 60 and other forms of enantioselective synthesis.

Conclusions
Cope rearrangements of chiral 9-BB cages simultaneously invert every stereogenic sp 3 -carbon centre of their structures. These configurational rearrangements occur rapidly and reversibly, achieving the uncommon property of dynamic sp 3 -carbon stereochemistry-one that has remained surprisingly rare since Le Bel 1 and van't Hoff 2 first identified tetrahedral carbon as a source of molecular chirality in 1874. Both the rate of sp 3 -carbon inversion and the equilibrium distribution of isomers are sensitive to changes in the 9-BB structure. On the one hand, the dynamics of the rearrangement processes are controlled through manipulation of covalent bonding or metal coordination of the 9-BB olefin groups, providing convenient functional handles. On the other hand, the cage adapts its configuration to minimize steric interactions with nearby fixed stereogenic elements and, in so doing, is able to transmit the stereochemical information across its rigid, tricyclic backbone. When interfaced with transition-metal complexes, the dynamic cage conveys a stereochemical preference to the chiral-at-metal 49,50 centre. Controllable and adaptable sp 3 -carbon stereochemistry of this kind can be exploited in enantioselective synthesis 7,9,10,30,45,62,63 and chiral functional materials 64 .

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